Finite Group Databasebeta

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D4×#13089678 #26041345

order11584
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#13089678

Splittings

SylowC181 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D181
commutatorC2×C181C22×C8
FittingC4×D4×C181C2
socleC22×C181C22×C4
prime radicalC2×D4×C181C4
cosocleC2×C4×C181C23
hypercenterC4×D4D181
hypocenterC181C8×D4
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C4×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#37532513, D8×#13089678, SD16×#13089678, …
maximal normal subgroup of#37532513, D8×#13089678, SD16×#13089678, …
maximal quotient ofD8×#13089678, SD16×#13089678, Q16×#13089678, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 615);